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  • 标题:Staticization-based representations for Schrödinger equations driven by Coulomb potentials
  • 本地全文:下载
  • 作者:William M. McEneaney ; Peter M. Dower
  • 期刊名称:IFAC PapersOnLine
  • 印刷版ISSN:2405-8963
  • 出版年度:2019
  • 卷号:52
  • 期号:7
  • 页码:25-32
  • DOI:10.1016/j.ifacol.2019.07.005
  • 语种:English
  • 出版社:Elsevier
  • 摘要:AbstractA stochastic control representation for the Maslov dequantization of the solution of the Schrödinger equation is obtained. The representation employs complex-valued diffusion process and stationarity of an action functional. The use of stationarity removes the need for convexity of the action, and hence there is no restriction on the duration of the problem. Previous efforts along this line were restricted to potentials which had holomorphic extensions to the entire space. The use of a stationarity based representation for the Coulomb potential removes that restriction. The result is a representation in terms of iterated staticization, which is expected to yield exceptional computational benefits.
  • 关键词:KeywordsSchrödinger equationHamilton-Jacobistationary actionstaticizationcomplex-valued diffusionleast actionstochastic processes
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